7 problems

Let $D_v$ denote the covariant derivative in the interior null direction $v$, let $\phi$ be the scalar field, and consider solutions of equations … . A quantity is oscillatory towa…

In the Einstein-scalar-field system outside spherical symmetry, consider a spacelike singularity $\mathcal{S}$ meeting a Cauchy horizon at a null-spacelike transition sphere. The g…

BKL scattering conjecture. Scattering at $tau to infty$ from the dynamical system defined by $\mathcal{A}$ to that defined by $\mathcal{E}_Phi$ defines a smooth map

Open-set conjecture. The image of the map from final data to initial data is an open set of anisotropic initial data.

Consider the lapse-scalar field system and its linearization around the backgrounds studied in the paper. The asymptotic data are functions naturally associated with the contractin…

Bounded $L^2$-curvature conjecture. The Einstein scalar field equations admit local Cauchy developments for initial data sets $(\Sigma,g,k,u_{0},u_{1})$ with locally finite $L^{2}$…

Non-spherical stability conjecture. Spherically symmetric locally BV-scattering dispersive solutions to the Einstein-scalar field equations are stable against non-spherically symme…